The Regular Army, O was performed by Harrigan and Hart, Words by Edward Harrigan. Music Adapted and Arranged by Dave Braham, published in 1874.

The version in the Digital Tradition is, as stated, from Loesser's Humor in American Song. There is sheet music at the Levy Sheet Music Collection. The Harrigan version is different from the DT version. It could be that a traditional version predates the Harrigan-Hart version.
-Joe Offer-